Fundamental Symmetries &

Neutrinos in Nuclear Science

M.J. Ramsey-Musolf

Wisconsin-Madison

http://www.physics.wisc.edu/groups/particle-theory/

NPACTheoretical Nuclear, Particle, Astrophysics & Cosmology

DOE , May 2010

Outline

1. Context: Fundamental Symmetries &

Neutrinos in Nuclear Physics

2. Challenges for the new Standard Model

3. The role of the “precision frontier”

4. CPV & the origin of baryonic matter

5. CP & T: EDMs

• Supersymmetry as an illustration

Low Energy Precision Tests : the

Standard Model

Observation of

parity-violation in60Co -decay: LH

nature of weak int

Searches for

neutron EDM: tinyQCD parameter:

axions?

Measurement of PV

asymmetry in eD scattering:

SU(2)LxU(1)Y prediction for

neutral currents

Measurements ofsuperallowed nuclear -

decay: most precise

determination of quark

mixing parameter

What are the symmetries of the “new Standard Model” ?

Rare Processes: Experiments

EDM Searches

• nucleon

• atoms

• leptons

0 Searches

• Cuore

• Exo

• Majorana

• SNO +

CLFV Searches

• mu2e

• PRIME

• EIC

Dark Matter Searches

• CLEAN

• WARP

Precision Tests: Experiments

Weak Decays

• n decay correlations

• nuclear decay

• pion decays

• muon decays

PV Electron Scattering

• Q-Weak

• 12 GeV Moller

• PV DIS

Muons

• gμ-2

• μA->eA

Neutrinos

• oscillations

• & decay

Torsion Balances

• Equiv Prin Tests

• Non-grav forces

EW Probes of QCD: Experiments

Hadronic PV

• FNPB/SNS

• NIST

PV Electron Scattering

• SAMPLE, G0,

HAPPEX, PVA4

• PREX

• PV DIS

EIC

•PVDIS

• CC DIS

• Why is there now more visible matter

than antimatter in the universe?

• What is the nature of the neutrinos,

what are their masses, and how have

they shaped the evolution of the

cosmos ?

• What are the unseen forces that were

present at the dawn of the universe but

disappeared from view as it evolved ?

Scientific Questions

Challenges for the New Standard Model

Symmetries & Cosmic History

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

QCD:

n+p nuclei

QCD:

q+g n,p…

Astro: stars,

galaxies,..

Symmetries & Cosmic History

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

to explain the microphysics of

the present universe

It utilizes a simple and elegant

symmetry principle

SU(3)c x SU(2)L x U(1)Y

• Big Bang Nucleosynthesis

(BBN) & light element

abundances

• Weak interactions in stars

& solar burning

• Supernovae & neutron

stars

Symmetries & Cosmic History

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

How is electroweak symmetry broken?

How do elementary particles get mass ?

Puzzles the St’d Model may or

may not solve:

SU(3)c x SU(2)L x U(1)Y

U(1)EM

• Non-zero vacuum

expectation value of

neutral Higgs breaks

electroweak sym and

gives mass:

• Where is the Higgsparticle?

• Is there more thanone?

CERN

Large Hadron Collider

Symmetries & Cosmic History

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

Puzzles the Standard Model can’t solve

1. Origin of matter

2. Unification & gravity

3. Weak scale stability

4. Neutrinos

What are the symmetries(forces) of the earlyuniverse beyond those ofthe SM?

SUSY ?

GUTS ?

Extra Dims ?WR

WL*

WL

~

The Role of the Precision Frontier

Searching for Symmetries of the New SM:

Two frontiers in the search

Collider experiments

(pp, e+e-, etc) at higher

energies (E >> MZ)

High energy

physics

Particle, nuclear

& atomic physics

CERN

Ultra cold neutronsLarge Hadron Collider

Indirect searches at

lower energies (E < MZ)

but high precision

Bumps Deviations

Unique role for low energy studies in the LHC era

Precision Probes of New Symmetries

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

Puzzles the Standard Model can’t solve

1. Origin of matter

2. Unification & gravity

3. Weak scale stability

4. Neutrinos

SUSY ?

GUTS ?

Extra Dims ?WR

WL*

WL

~

μ

μ

˜ 0

˜ μ

˜ μ

e

W

e

Precision Probes of New Symmetries

Standard Model Universe

EW Symmetry

Breaking: Higgs ?

New Forces ?

Puzzles the Standard Model can’t solve

1. Origin of matter

2. Unification & gravity

3. Weak scale stability

4. Neutrinos

SUSY ?

GUTS ?

Extra Dims ?WR

WL*

WL

~

μ

μ

˜ 0

˜ μ

˜ μ

e

W

e

?

Precision & Energy Frontiers

Radiative

corrections

Direct

Measurements

J. Ellison, UCI

GFZ

GFμ

1+ rZ rμ( )

t

t Z 0 Z 0

t

b W + W +

Precision & Energy Frontiers

Radiative

corrections

Direct

Measurements

Stunning SM Success

J. Ellison, UCI

GFZ

GFμ

1+ rZ rμ( )

t

t Z 0 Z 0

t

b W + W +

• Precision measurementspredicted a range for mt

before top quark discovery

• mt >> mb !

• mt is consistent with thatrange

• It didn’t have to be thatway

Precision & Energy Frontiers

Radiative

corrections

Direct

Measurements

Stunning SM Success

J. Ellison, UCI

GFZ

GFμ

1+ rZ rμ( )

t

t Z 0 Z 0

t

b W + W +

• Precision measurementspredicted a range for mt

before top quark discovery

• mt >> mb !

• mt is consistent with thatrange

• It didn’t have to be thatway

Probing Fundamental

Symmetries beyond

the SM:

Use precision low-

energy measurements

to probe virtual effects

of new symmetries &

compare with collider

results

Precision ~ Mass Scale

NEW =ONEW

OSM

M˜ M

2 M=mμ ~ 2 x 10-9

exp ~ 1 x 10-9

M=MW ~ 10-3

Interpretability

• Precise, reliable SM predictions

• Comparison of a variety of observables

• Special cases: SM-forbidden or suppressed processes

Precision Probes of the New SM

Discovery

Precision ~ Mass Scale

NEW =ONEW

OSM

M˜ M

2 M=mμ ~ 2 x 10-9

exp ~ 1 x 10-9

M=MW ~ 10-3

Interpretability

• Precise, reliable SM predictions

• Comparison of a variety of observables

• Special cases: SM-forbidden or suppressed processes

Precision Probes of the New SM

Discovery

Illustrate ideas, physics reach,

& developing theoretical

methods with Minimal

Supersymmetric SM (MSSM)

but more generally applicable

EDMs & the Origin of Baryonic Matter

What is the Origin of Matter

?

Baryogenesis: When?

CPV? SUSY? Neutrinos?

EW Baryogenesis:

testable w/ EDMs +

colliders

Leptogenesis:

less testable,

look foringredients w/ s

Can new TeV scale

physics explain the

abundance of matter ?

If so, how will we

know ?

Baryogenesis: Ingredients

Anomalous B-violating processes

Prevent washout by inverse processes

Sakharov Criteria

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

SM Sphalerons:

SM CKM CPV:

SM EWPT:

EDMs

LHC: Scalars

Baryogenesis: New Electroweak Physics

Weak Scale Baryogenesis

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

new

(x)

Unbroken phase

Broken phaseCP Violation

Topological transitions

1st order phase transition

g

g

e-

new

new

new

AA

Baryogenesis: New Electroweak Physics

Weak Scale Baryogenesis

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

new

(x)

Unbroken phase

Broken phaseCP Violation

Topological transitions

1st order phase transition

g

g

e-

new

new

new

• Is it viable?

• Can experiment constrain it?

• How reliably can we compute it?

Theoretical Issues:

Strength of phase transition (Higgs sector)

Bubble dynamics (numerical)

Transport at phase boundary (non-eq QFT)

EDMs: many-body physics & QCD

AA

Baryogenesis: EW Phase Transition

Weak Scale Baryogenesis

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

new

(x)

Unbroken phase

Broken phase

CP Violation& Transport1st order phase transition

Profumo, Shaugnessy, MR-M, Patel…

F F

Increasing mh

1st order 2nd order

Adding new

scalar particles

to the SMBarger, Fileviez-Perez,

Langacker, McCaskey,

O’Connel, Patel, Profumo, R-M,

Shaugnessy, Wang, Wise

Scalar Dark

Matter?

…Gonderinger,

Li, Patel, R-M

Baryogenesis: CPV & Transport

Weak Scale Baryogenesis

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

new

(x)

Unbroken phase

Broken phase

CP Violation& Transport

Topological transitions

MSSM: Chung, Garbrecht, R-M, Tulin ‘09

Bubble interior

Bubble exterior

LH leptons

LH quarksLH fermions

CPV

Transport: A Competition

CPV

Chem Eq

R-M et al

Diffusion

Also Cirigliano,

Lee, R-M, Tulin

Coupled set of (~30) quantum Boltzmann equations

Baryogenesis: CPV & Transport

Weak Scale Baryogenesis

• B violation

• C & CP violation

• Nonequilibrium

dynamics

Sakharov, 1967

new

(x)

Unbroken phase

Broken phase

CP Violation& Transport

Topological transitions

MSSM: Chung, Garbrecht, R-M, Tulin ‘09

Bubble interior

Bubble exterior

LH leptons

LH quarksLH fermions

CPV

Transport: A Competition

CPV

Chem Eq

R-M et al

Diffusion

Also Cirigliano,

Lee, R-M, Tulin

EDM searches:

How strong was the CPV “kick” ?

Details of spectrum impt: LHC !

Chung, Garbrecht, R-M, Tulin ‘08

Probing CP &T: Electric Dipole Moments

EDMs: New CPV?

• SM “background”

well below new

CPV expectations

• New expts: 102 to

103 more sensitive

• CPV needed for

BAU?3.1 x 10-29

r E

r d = d

r S

EDM =

dr S

r E

h

T-odd , CP-oddby CPTtheorem

r E

r d = d

r S

EDM =

d (r S )

r E

h

T-odd , CP-oddby CPTtheorem

EDM =

dr S

r E

h

T-odd , CP-oddby CPTtheorem

r E

r d = d

r S

r B

EDM =

dr S (

r E )

h

T-odd , CP-oddby CPTtheorem

r E

r d = d

r S

r B

x

dn: x < 0.5 mm

C-Y Liu

EDMs: Standard Model CKM

3.1 x 10-29

CKM CPV

• 1 loop vanishes

( ~ Vus Vus* )

• 2 loop shown to

vanish explicitly

u

sW +

W +

n

pK +

K +

np

K +

• Khriplovich et al;

McKellar…

• Donoghue, Holstein,

RM; Khriplovich et al

Penguin: S = 1

EDMs: Standard Model -term

3.1 x 10-29

n

p+

+

np

+

• Crewther et al; van

Kolck et al ; Herczeg

• Haxton & Henley;

Engel;

L QCD

• vanishes for any

mq=0

• “bar” : absorb quark

field redefinition

dn & dA (199Hg):

Peccei -Quinn Sym?

EDMs: Peccei-Quinn & Axions I

Axion Field: GB of Spont Broken U(1)PQ

Chiral Anomaly:

a a + a

-term

+a

fa+

a

faObserved ~ 0

Axion

EDMs: Peccei-Quinn & Axions II

+a

fa+

a

fa

Observed ~ 0

Axion

Dark Matter

Solar

EDMs: New CPV?

• SM “background”

well below new

CPV expectations

• New expts: 102 to

103 more sensitive

• CPV needed for

BAU?

Mass Scale Sensitivity

e

sin CP ~ 1 M > 5000 GeV

M < 500 GeV sin CP < 10-2

3.1 x 10-29

EDMs: New CPV?

• SM “background”

well below new

CPV expectations

• New expts: 102 to

103 more sensitive

• CPV needed for

BAU?

Mass Scale Sensitivity

e

sin CP ~ 1 M > 5000 GeV

M < 500 GeV sin CP < 10-2

3.1 x 10-29

EDMs: Complementary Searches I

f

˜ 0

˜ f

˜ f

g

q

˜ 0˜ q

˜ q

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

EDMs: Complementary Searches II

f

˜ 0

˜ f

˜ f

g

q

˜ 0˜ q

˜ q

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

CJ

TMJ

TEJ

P T P T P T P T

E O

O E

O E

Nuclear Moments

EDM, Schiff…

MQM….

Anapole…

Nuclear

Enhancements

EDM Interpretation & Multiple Scales

BSM CPV

SUSY, GUTs, Extra Dim…

EW Scale Operators

Had Scale Operators

Baryon Asymmetry

Early universe CPV

Nuclear & atomic MEs

Schiff moment, other P- &

T-odd moments, e-nucleus

CPV

Collider Searches

Particle spectrum; also

scalars for baryon asym

QCD Matrix Elements

dn , g NN , …

Expt

EDM Interpretation & Multiple Scales

BSM CPV

SUSY, GUTs, Extra Dim…

EW Scale Operators

Had Scale Operators

Baryon Asymmetry

Early universe CPV

Nuclear & atomic MEs

Schiff moment, other P- &

T-odd moments, e-nucleus

CPV

Collider Searches

Particle spectrum; also

scalars for baryon asym

QCD Matrix Elements

dn , g NN , …

Expt

Had Scale Operators

Also QCD term

SM particles onlyBSM: new physics scale

C: model-dep op coeffs

e, q, g, (no Higgs)

QCD evolution

EDMs: QCD & Many-Body Theory I

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

EDMs: QCD & Many-Body Theory I

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

Neutron EDM from LQCD:

Two approaches:

• Expand in & average overtopological sectors (Blum et al,Shintani et al)

• Compute E for spin up/downnucleon in background E field(Shintani et al)

mN=2.2 GeV

QCD SR (Pospelov et al)

EDMs: QCD & Many-Body Theory II

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

+L

n

p

+L

Hadronic couplings

Pospelov, Ji et al:

PCAC + had

models & QCD SR

ChPT for dn: van Kolck et al

P-,T-odd NN

I = 0,1,2

EDMs: QCD & Many-Body Theory III

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

+L

n

p

+L

Nuclear Schiff Moment

Nuclear EDM: Screened in atoms

Schiff Screening

Atomic effect from

nuclear finite size:

Schiff moment

EDMs: QCD & Many-Body Theory III

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

Electron

Improvements

of 102 to 103

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

N e

QCD

QCD

QCD

+L

n

p

+L

Nuclear Schiff Moment

Nuclear EDM: Screened in atoms

Schiff Screening

Atomic effect from

nuclear finite size:

Schiff moment

Liu et al: New formulation of Schiff operator

+ …

Role of nuclear correlations

EDMs & Schiff Moments

f

˜ 0

˜ f

˜ f

g

q

˜ 0˜ q

˜ q

One-loop

EDM: q, l, n… Chromo-EDM: q, n…

+L

Dominant in

nuclei & atoms

Engel & de Jesus: Enhanced isoscalar sensitivity ( QCD )

Schiff Moment in 199Hg Nuclear & hadron structure

EDMs & Isospin Filter: n, p, A

Chiral limit:

Nucleons Schiff Moments

+L

Schiff Moment in 199Hg

n

p

p

n

+

+

dn dp ~ g 0 dn + dp ~ g 1

EDMs BSM: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Universality Assumption

1 = 2= 3

Common A

EDMs BSM: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

EWSB

Quark & Lepton EDMs

EDMs BSM: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Quark Chromo-EDMs

EDMs BSM: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Weinberg 3 gluon Op

EDMs BSM: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Four fermion Ops

MSSM EDMs: Leading Contributions

f

˜ 0

˜ f

˜ f

g

q

˜ 0˜ q

˜ q

Electron

Neutronf

˜ 0

˜ f

˜ f

Neutral

Atomsg

q

˜ 0˜ q

˜ q

Deuterong

q

˜ 0˜ q

˜ q

g

gg

g

gg

g

gg

q, l EDM Chromo-

EDM

Weinberg

3 gluon

Heavy Sfermions: Two-loop EDMs

One loop EDMs suppressed in heavy

sfermion regime

Li, Profumo, R-M: PRD 78:075009

(2008)

WH Loops dominate for neutron &comparable to H, A for electron

mA=300 GeV, μ=300 GeV, M2=2M1=290 GeV

EDM Interpretation: MSSM

A = arg (Af Mj )

Ritz CIPANP 09

1-loop: Universal Phases

j = arg (μMjb*)Universality Assumption

1 = 2= 3

Common A

EDM Interpretation: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Correlated Constraints

PresentFuture dn : 100 x

present sensitivity

Li, Profumo, R-M ‘10

EDM Interpretation: MSSM

A = arg (Af Mj )

j = arg (μMjb*)

Correlated Constraints

PresentFuture dn : 100 x

present sensitivity

Li, Profumo, R-M ‘10

EDM Interpretation: MSSM at 2 Loop

A = arg (Af Mj )

Li, Profumo, R-M 09

2-loop: Non-universal Phases

j = arg (μMjb*)

f

˜ 0

˜ f

˜ f

g

q

˜ 0˜ q

˜ q

Decouple in heavy

sfermion regime

One Loop EDMs & Baryogenesis

g

q

˜ 0˜ q

˜ q

f

˜ 0

˜ f

˜ f

new

(x)

q , ˜ W , ˜ B , ˜ H u,d

T ~ TEW

Resonant Non-resonantCirigliano, Lee,

Tulin, R-M

Future

de dn dA

EDMs & EWB: 2 Loop Regime

Arg(μM1b*) = Arg(μM2b

*)/

Weak dependence ofde , dn on Arg(μM1b

*)

Res + EWB not

compatible with dn

Res & non-res 0

EWB compatible

with future dn , light

mA, & moderatetan

Li, Profumo, R-M: PLB

673:95 (2009)

EDM Interpretation & Multiple Scales

BSM CPV

SUSY, GUTs, Extra Dim…

EW Scale Operators

Had Scale Operators

Baryon Asymmetry

Early universe CPV

Nuclear & atomic MEs

Schiff moment, other P- &

T-odd moments, e-nucleus

CPV

Collider Searches

Particle spectrum; also

scalars for baryon asym

QCD Matrix Elements

dn , g NN , …

Expt

LHC phenomenology

B Physics

Dark Matter

EW Baryogenesis

Quantum transport

theory

MSSM Baryogenesis: EDMs & LHC

baryogenesis

Present de

LEP II excl

Prospective dn

Cirigliano, Profumo, R-M

+-driven EWB

0-driven EWB

LHC reach

MSSM Baryogenesis: EDMs & LHC

baryogenesis

Present de

LEP II excl

Prospective dn

Cirigliano, Profumo, R-M

+-driven EWB

0-driven EWB

LHC reach

New complete 2-loop MSSM EDM: Li, Profumo, R-M

MSSM Baryogenesis: EDMs & LHC

baryogenesis

Present de

LEP II excl

Prospective dn

Cirigliano, Profumo, R-M

+-driven EWB

0-driven EWB

10-28

LHC reach

B Physics

FBMSSM: only A

Altmannshofer et al, PLB 669, 239 (2008)

Af t( ) = S f sin m t( ) Cf cos m t( )

Future dn,e

Relationship to JLab PVES

J Lab PVES: Insensitive to CPV but probes mass scale

r e

e

e , p

e , pZ 0

r e

e

e , p

e , p

APV =N N

N + N=GFQ

2

4 2QW + F(Q

2, )[ ]

˜ e

˜ e +

+L+

e f

Z 0˜

˜ +

e

e

ef

f

fZ 0

SUSY Loops: Kurylov, SU, MR-M How heavy are

the sfermions?

Probing SUSY with PV Electron Scattering

QW

P,

SU

SY

/

QW

P,

SM

RPV: No SUSY DMMajorana s

SUSY Loops

QWe, SUSY / QW

e, SM

gμ-2

12 GeV

6 GeV

E158

Q-Weak (ep)

Moller (ee)

Kurylov, RM, Su

Probing Sfermion Mass Scale

˜ e

˜ e +

+L+

e f

Z 0˜

˜ +

e

e

ef

f

fZ 0

SUSY Loops: Kurylov, SU, MR-M

Su, R-M

Preliminary

Contours ofconstant QW

e

EDMs: What We May Learn

Present n-EDM limit

Proposed n-EDM limit

?

Matter-Antimatter

Asymmetry in

the Universe

Better theory ?

New theory ?

Leptogenesis ?

“n-EDM has killed

more theories than

any other single

experiment”

Summary & Outlook I

1. NP studies of FS & ’s are poised to provide key

ingredients of the new Standard Model

2. EDM searches may discover the CPV needed to

explain the origin of baryonic matter

3. Sensitivity of EDMs exceeds that of LHC & B-physics

program, but HEP experiments provide

complementarity information

4. Comprehensive search strategy involving a variety of

systems is crucial

5. Ongoing theory work essential to guide the EDM

program, properly interpret results in terms of the new

Standard Model, and delineate broader implications

Summary & Outlook II

1. Nucleon & lepton EDM searches with a sensitivity of ~

10-28 e-cm needed to conclusively probe MSSM

baryogenesis

2. Theoretical tasks include:

• Complete development of tools for robustbaryogenesis calculations (transport, EWPT)

• Up-dated calculations of nuclear Schiff momentsand other P,T-odd moments

• Refined hadronic computations of dn,p and P,T-odd pion-nucleon couplings

• Apply to other BSM scenarios

• Delineate comprehensively relation with future B-physics and LHC studies

Back Matter

SUSY Radiative Corrections

Propagator

Box

Vertex &

External leg

˜ e

˜ e +

+L+

e f

Z 0˜

˜ +

e

e

ef

f

fZ 0

˜ 0

˜ e

˜

˜

+ +L

e

e

e

e

f

f

f

fZ 0 Z 0

˜ e

˜ e

˜ e +L

e

e

f

f

˜ f

˜

˜

Kurylov, RM, Su

SUSY: R Parity-Violation

μ

e e

μ

˜ e Rk

12k 12k

e

d e

d

˜ q Lj

/1j1

/1j1

L=1 L=1

12k =12k

2

4 2GF M˜ e R

k

2 1j 1/

=iji/ 2

4 2GFM˜ q L

j

2